Dynamics of infectious disease models on network with drug-resistant strain and saturated incidence

Abstract Antibiotics are frequently used to treat diseases caused by microbial infections. However, their continuous abuse has given rise to highly drug-resistant strains, posing a great challenge to disease prevention and control. Therefore, this paper constructs a network SIR epidemic model with drug-resistant strains and a saturated incidence rate, dividing the population into three categories: susceptible, infected, and recovered. In multi-strain ecosystems, saturated incidence effectively reveals competitive and cooperative effects during multi-strain community evolution. This mechanism constrains the infinite growth of new infections through factors such as enhanced public protection and limited contact opportunities. We derived the transmission threshold for this model. Analysis revealed that the model has only three equilibria, and there is no wild-type strain-dominant boundary equilibrium due to the strain transformation mechanism. Simultaneously, the stability of each equilibrium was demonstrated. The study shows that the saturated incidence rate significantly affects the stability of the equilibrium of drug-resistant strain, and the dynamic transformation of strains exerts a fundamental influence on the existence of positive equilibrium. Numerical simulations verify the theoretical results, indicating that suppressing the emergence of drug-resistant strains is the key to controlling such infectious diseases, and strict control of antibiotic use is an important strategy to prevent their spread.